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Properties of the four families of recently introduced special functions oftwo real variables, denoted here by $E^\pm$, and $\cos^\pm$, are studied. Thesuperscripts $^+$ and $^-$ refer to the symmetric and antisymmetric functionsrespectively. The functions are considered in all details required for theirexploitation in Fourier expansions of digital data, sampled on square grids ofany density and for general position of the grid in the real plane relative tothe lattice defined by the underlying group theory. Quality of continuousinterpolation, resulting from the discrete expansions, is studied, exemplifiedand compared for some model functions.

Two-dimensional symmetric and antisymmetric generalizations of exponential and cosine functions